confluent hypergeometric equation

confluent hypergeometric equation的基本解释

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合流超几何方程

与confluent hypergeometric equation相关的网络例句 [注：此内容来源于网络，仅供参考]

In this topic, the dynamic analysis methods for piezoelectric vibrator are studied systematically based on the theoretical model, FEM numerical experimentation and FEM governing equation for given compound-mode vibrator, and some valuable conclusions are obtained. The main work accomplished is summarized as follows: 1.Elaborate the main modeling methods for piezoelectric vibrator and the significance and necessity to study the dynamic characteristics of piezoelectric vibrator which emphasize the urgency of this paper. 2.Take the bending deformation induced by piezoelectric ceramic as example, the energy transfer mechanism of electric energy to mechanical energy are analyzed; the motion and force transfer mechanism are analyzed for the longitudinal-bending vibrator. 3.Based on mode assumption and Hamilton principle, the coupling model of piezoelectric vibrator of linear USM is built; moreover, the equivalent circuit model is obtained and a coupling equation represents the relation between electric parameters and mechanical parameters is derived which provides foundation to match the vibrator and driving circuit. 4.Combine the constitutive equation of piezoelectric ceramic with elastic-dynamical equation, geometric equation in force field and the Maxwell equation in electric field and the corresponding boundary condition equation, the FEM control equation for piezoelectric vibrator of USM to solve dynamic electro-mechanical coupling field is established by employing the principle of virtual displacement. The equation lays the foundation to study the non-linear constitutive equation of piezoelectric ceramic driven by high-power. 5.Define the dynamic indexes of characteristic of vibrator and carry out variable parameters simulation by calculating the model parameters and the electric characteristics of vibrator are simulated according to the equivalent circuit model. By numerical experimentation, the working mode of vibration of vibrator and the shock excitation results of the working frequency band which provides the mode frequency to realize bimodal are analyzed. Detailed calculation of the electro-mechanical coupling field parameters is made by programming the FEM control equation.

本课题从理论模型、有限元数值试验、有限元控制模型等方面以复合振动模式振子为例对超声电机压电振子的动力学特性及其分析方法进行了全面系统地研究，得出了许多有价值的结论，主要概括如下： 1、阐述了目前针对超声电机压电振子的主要建模方法，对压电振子动态特性的研究意义和必要性进行了论述，突出了本文研究内容的迫切性； 2、以压电陶瓷诱发弹性体发生弯曲变形为例，分析了压电陶瓷通过诱发应变来实现机电能量转换的机理；对基于纵弯模式的压电振子的运动及动力传递机理进行了分析； 3、基于模态假定，利用分析动力学的Hamilton原理，建立了面向直线超声电机压电振子的机电耦合动力学模型，并据此建立了压电振子的等效电路模型，导出了电参量与动力学特性参量的耦合方程，为压电振子与驱动电路的匹配提供了依据； 4、从压电陶瓷的本构方程出发，综合力场的弹性动力学方程、几何方程、电场的麦克斯韦方程以及相应的边界条件方程，采用虚位移原理，建立了压电振子动态问题机电耦合场求解的有限元控制方程，为研究其大功率驱动下的非线性本构模型奠定了基础； 5、界定压电振子的动力学特性指标，对压电振子的机电耦合动力学模型参数进行计算及变参数仿真；依据等效电路模型，对压电振子的电学特性进行了仿真分析；通过有限元数值实验，对压电振子工作模态附近的模态振型及工作频率附近的频段进行了激振效果分析，找出了实现模态简并的激振频率；利用有限元控制方程，通过编程计算，对压电振子的力电耦合场参数进行了详细计算，得出了一些有价值的结论。

Several important nonlinear equations of mathematical physics such as φ4 equation, Klein-Gordon equation, the approximate equations of sine-Gordon equation and sinhGordon equation, Landau-Ginzburg-Higgs equation, Duffing equation, nonlinear telegraph equation are the special cases of the nonlinear wave equation presented in this paper.

几个有重要应用的非线性数学物理方程，如矿方程，Klein-Gordon方程，Sine-Gordon方程，及Sinh-Gordon方程的近似，Landau-Ginzburg-Higgs方程，Duffing方程，非线性电报方程等都可作为该方程的特殊情形得到相应的显式精确解，这里方法也可推广到n+1维空间情形。

The quasi-analytical expressions of the relative concentrations at the mobile region and the immobile region are deduced respectively by using hypergeometric equation, hypergeometric function and the method of Laplace transform under the initial concentration zero and the first or second boundary condition of a semi-infinite one-dimensional space.

并分别在初始浓度为零，半无限一维空间内第一类边界条件和第二类边界条件下，利用超几何方程、超几何函数和Laplace变换法推导出了可动区和不动区溶质相对浓度的准解析表达式。

与confluent hypergeometric equation相关的网络解释 [注：此内容来源于网络，仅供参考]

confluent hypergeometric equation：合镣超几何微分方程

confluent divided difference 合六差 | confluent hypergeometric equation 合镣超几何微分方程 | confluent hypergeometric function 合连几何函数

confluent hypergeometric equation：合流超几何方程;合流超比方程

合流分析 confluence analysis | 合流超几何方程;合流超比方程 confluent hypergeometric equation | 合流超几何函数;合流超比函数 confluent hypergeometric function

confluent hypergeometric equation：汇合型超几何方程

汇点|sink | 汇合型超几何方程|confluent hypergeometric equation | 汇合型超几何函数|hypergeometric function of confluent type

confluent hypergeometric equation：群集超几何方程式

"confluent band-pass filter","汇合带通滤波器" | "confluent hypergeometric equation","群集超几何方程式" | "confocal resonator","共焦共振器"